Transformations of Feynman integrals under nonlinear transformations of the phase space

Journal Article · Sun Jan 01 04:00:00 EST 1995 · Theoretical and Mathematical Physics

OSTI ID:390969

Smolyanov, O G; Smolyanova, M O ^[1]

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1. Moscow State Univ. (Russian Federation)

The Feynman measure is defined as a linear continuous functional on a test-function spare (introduced in the paper). The functional is given by means of its Fourier transform. Not only a positive-definite correlation operator but also one without fixed sign is considered (the latter case corresponds to the so-called symplectic, or Hamiltonian, Feynman measure). The Feynman integral is the value of the Feynman measure on a function (in the test-function space). The effect on the Feynman measure of nonlinear transformations of the phase space in the form of shifts along vector fields or along integral curves of vector fields is described. Analogs of the well-known Cameron-Martin, Girsanov-Maruyama, and Ramer formulas in the theory of Gaussian measures are obtained. The results of the paper can be regarded as formulas for a change of variable in Feynman integrals.

• OSTI ID: 390969
• Journal Information: Theoretical and Mathematical Physics, Journal Name: Theoretical and Mathematical Physics Journal Issue: 1 Vol. 100; ISSN 0040-5779; ISSN TMPHAH
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
DISTRIBUTION
FEYNMAN PATH INTEGRAL
FOURIER TRANSFORMATION
NONLINEAR PROBLEMS
PHASE SPACE